// Copyright (c) 2009 libmv authors. // // Permission is hereby granted, free of charge, to any person obtaining a copy // of this software and associated documentation files (the "Software"), to // deal in the Software without restriction, including without limitation the // rights to use, copy, modify, merge, publish, distribute, sublicense, and/or // sell copies of the Software, and to permit persons to whom the Software is // furnished to do so, subject to the following conditions: // // The above copyright notice and this permission notice shall be included in // all copies or substantial portions of the Software. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS // IN THE SOFTWARE. #include <cstdio> // TODO(keir): This code is plain unfinished! Doesn't even compile! #include "libmv/base/vector.h" #include "libmv/multiview/fundamental_kernel.h" #include "libmv/numeric/numeric.h" #include "libmv/numeric/poly.h" #include "libmv/logging/logging.h" namespace libmv { namespace fundamental { namespace kernel { void SevenPointSolver::Solve(const Mat &x1, const Mat &x2, vector<Mat3> *F) { assert(2 == x1.rows()); assert(7 <= x1.cols()); assert(x1.rows() == x2.rows()); assert(x1.cols() == x2.cols()); // Set up the homogeneous system Af = 0 from the equations x'T*F*x = 0. MatX9 A(x1.cols(), 9); EncodeEpipolarEquation(x1, x2, &A); // Find the two F matrices in the nullspace of A. Vec9 f1, f2; Nullspace2(&A, &f1, &f2); Mat3 F1 = Map<RMat3>(f1.data()); Mat3 F2 = Map<RMat3>(f2.data()); // Then, use the condition det(F) = 0 to determine F. In other words, solve // det(F1 + a*F2) = 0 for a. double a = F1(0, 0), j = F2(0, 0), b = F1(0, 1), k = F2(0, 1), c = F1(0, 2), l = F2(0, 2), d = F1(1, 0), m = F2(1, 0), e = F1(1, 1), n = F2(1, 1), f = F1(1, 2), o = F2(1, 2), g = F1(2, 0), p = F2(2, 0), h = F1(2, 1), q = F2(2, 1), i = F1(2, 2), r = F2(2, 2); // Run fundamental_7point_coeffs.py to get the below coefficients. // The coefficients are in ascending powers of alpha, i.e. P[N]*x^N. double P[4] = { a*e*i + b*f*g + c*d*h - a*f*h - b*d*i - c*e*g, a*e*r + a*i*n + b*f*p + b*g*o + c*d*q + c*h*m + d*h*l + e*i*j + f*g*k - a*f*q - a*h*o - b*d*r - b*i*m - c*e*p - c*g*n - d*i*k - e*g*l - f*h*j, a*n*r + b*o*p + c*m*q + d*l*q + e*j*r + f*k*p + g*k*o + h*l*m + i*j*n - a*o*q - b*m*r - c*n*p - d*k*r - e*l*p - f*j*q - g*l*n - h*j*o - i*k*m, j*n*r + k*o*p + l*m*q - j*o*q - k*m*r - l*n*p, }; // Solve for the roots of P[3]*x^3 + P[2]*x^2 + P[1]*x + P[0] = 0. double roots[3]; int num_roots = SolveCubicPolynomial(P, roots); // Build the fundamental matrix for each solution. for (int kk = 0; kk < num_roots; ++kk) { F->push_back(F1 + roots[kk] * F2); } } //template<bool force_essential_constraint> void EightPointSolver::Solve(const Mat &x1, const Mat &x2, vector<Mat3> *Fs) { assert(2 == x1.rows()); assert(8 <= x1.cols()); assert(x1.rows() == x2.rows()); assert(x1.cols() == x2.cols()); MatX9 A(x1.cols(), 9); EncodeEpipolarEquation(x1, x2, &A); Vec9 f; Nullspace(&A, &f); Mat3 F = Map<RMat3>(f.data()); // Force the fundamental property if the A matrix has full rank. if (x1.cols() > 8) { Eigen::JacobiSVD<Mat3> USV(F, Eigen::ComputeFullU | Eigen::ComputeFullV); Vec3 d = USV.singularValues(); d[2] = 0.0; F = USV.matrixU() * d.asDiagonal() * USV.matrixV().transpose(); } Fs->push_back(F); } } // namespace kernel } // namespace fundamental } // namespace libmv